OK good, this helps.
A few things I have run into over the years and will pass on.
1. Tires, can make or break a good towing setup. The good news, you are still on the stock F250 setup.
2. There is "something" about the new rubber compounds in many brands of tires that create what is nicknamed, "squirm" to some. It is the feeling inside the truck that the whole truck is moving around where it never used to. It does not feel good to you once you had a perfect towing before.
3. The Michelin LTX tire, even in LT tires, has a softer side wall flex then other brands. I had the first generation of the LTX on my 2500 Suburban as a replacement tire and that event took a stable towing truck into one that shifts hard when wind gust hit it. The same tire on a F250 with a Hensley can do the same thing given the right circumstances.
In order to address the LTX issues, at least the 1st generation of them, you had to up the air pressure in the tire above door sticker to get them to tame down. The 2500 Suburban which had 50 psi front and 80 psi back on the door sticker, worked great on the stock Uniroyal Steel Tex tire. That same pressure on the LTX would allow the front of the truck to shift when hard wind gusts would hit the rig and create an instability in the truck that was very noticeable. My wife even jumped in and said "What was that?" After learning and experimenting, 60 psi was a global shift in truck stability. 70 psi in that truck was too hard, the whole truck bounced to the left or right over a railroad truck or other hard bump. I settled on 65psi and ran it until the F350 came and we changed campers.
I know there is a very good moderator on this thread, that ran the original LTX on his older F250 with the Power Stroke diesel and ran them at 70psi. Same tire as I had. He would swear by the LTX while I was swearing at them...;) Point is, his heavy front end needed the 70psi and he never found the issue I did. My other good friend from that era had his F250 gasser with a Hensley and the just changed from the Steel Tex to LTX and he never upd'ed the air pressure. He was on 50psi tires on the front, I told him, air them up, he didn't and he came back with, wow I thought I was about to loose it in a 30 mph turn. He learned too, aired them and the problem went away.
The LTX has changed since the original, but they are still a softer sidewall tire. Your door sticker lists the pressure for max load of the truck axles they declare them too. You running 5psi under means you do not have the full load capacity of the truck, and you may not need it for load carrying, but it is something to keep in mind. The tire will be slightly softer and flex slightly more 5 psi under.
New tire squirm, this is real and there is no real good way to know it before you buy. There is no rating for it. It affects Dodge, GM and Ford trucks and any other 3/4 or 1 ton. I have spoke to two different tire engineers on this is they tell me it is not mold release and I never got a real answer. But this issue hit my F350 on my 3rd set of tires. A few years ago on the same exact Continental Conti Trac TR tires the truck came with, the truck handling was unstable as soon as the new tires went on. The higher winds was the issue. A 32 ft camper is a big sale, but this rig was rock solid until the new tires came. The first 2 sets I had no issues. This last 3rd set, I have this unstable feeling again. I went through the WD hitch, I'm at 16% TW, the end result, after 4,000 miles on the new tires the truck is back to normal. Some people have reported the issue goes away in 2,000 miles. I started to notice a difference at 2,000 miles, but it took until 4,000 miles the issue totally went away. There are other reports like this on new tire on the forum. Something with the newer way tires are made, this issue shows up.
You may be into the new tire squirm issue. The 75 psi on the LTX may aggravate it some, not sure but it is something you can adjust.
The helper spring in the back, see here on mine, the rear end of the spring is just kissing the upper frame bracket. The front lower end of the spring is not touching.
A learning, until I got my truck bed loads and camper TW dialed in with the WD, I would have closer to unloaded weight on the front of the truck. This is an 2005 truck which is before all the newer SAE front axle load restoration talks started. With the truck bed lightly loaded, and the camper too, the rear helper spring never touched the frame bracket. There was not enough weight. That allowed the camper to push the truck left to right more, it was not very stable. Wind really had nothing to do with this. I fully loaded all my stuff, 500#, in the truck bed, and in the camper, now 1,500# TW, reset the WD hitch to be about 150# light on the front end, and the then the rear helper spring kissed the frame bracket. The truck took a global shift in stability left to right. The springs against the frame bracket act like a roll bar and the truck became one very stable rig.
I think the new tires are a big part of the problem until they get wore in. That sticks out like a sore thumb.
Hope this helps.
John